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We derive and demonstrate new methods for dewarping images depicted in convex mirrors in artwork and
for estimating the three-dimensional shapes of the mirrors themselves. Previous methods were based on the
assumption that mirrors were spherical or paraboloidal, an assumption unlikely to hold for hand-blown glass
spheres used in early Renaissance art, such as Johannes van Eyck's Portrait of Giovanni (?) Arnolfini and his
wife (1434) and Robert Campin's Portrait of St. John the Baptist and Heinrich von Werl (1438). Our methods
are more general than such previous methods in that we assume merely that the mirror is radially symmetric
and that there are straight lines (or colinear points) in the actual source scene. We express the mirror's shape
as a mathematical series and pose the image dewarping task as that of estimating the coefficients in the series
expansion. Central to our method is the plumbline principle: that the optimal coefficients are those that dewarp
the mirror image so as to straighten lines that correspond to straight lines in the source scene. We solve for
these coefficients algebraically through principal component analysis, PCA. Our method relies on a global figure
of merit to balance warping errors throughout the image and it thereby reduces a reliance on the somewhat
subjective criterion used in earlier methods. Our estimation can be applied to separate image annuli, which is
appropriate if the mirror shape is irregular. Once we have found the optimal image dewarping, we compute
the mirror shape by solving a differential equation based on the estimated dewarping function. We demonstrate
our methods on the Arnolfini mirror and reveal a dewarped image superior to those found in prior work|an
image noticeably more rectilinear throughout and having a more coherent geometrical perspective and vanishing
points. Moreover, we find the mirror deviated from spherical and paraboloidal shape; this implies that it would
have been useless as a concave projection mirror, as has been claimed. Our dewarped image can be compared to
the geometry in the full Arnolfini painting; the geometrical agreement strongly suggests that van Eyck worked
from an actual room, not, as has been suggested by some art historians, a "fictive" room of his imagination. We
apply our method to other mirrors depicted in art, such as Parmigianino's Self-portrait in a convex mirror and
compare our results to those from earlier computer graphics simulations.
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